Darpana solved the equation s = a+b+c/3 for a. Her steps are shown below:
1. Multiply by 3: s=a+b+c/3
3s=a+b+c

2. Subtract b: 3s-b=a+b+c-b
3s-b=a+c
3. Divide by c: 3s-b/c=a
Which statement about Darpana’s work is true?
In step 1 she needed to divide by 3 rather than multiply.
In step 2 she needed to add b rather than subtract.
In step 3 she needed to subtract c rather than divide.
Darpana solved the equation correctly.

ANSWER

The height is 6 units.

The base is 2 units.

EXPLANATION

The given rectangle has vertices (–4, 7), (–2, 7), (–2, 1), and (–4, 1).

To find the height of the rectangle, we use the points (-2,7) and (-2,1) or

(-4,7) and (-4,1) because they form the vertical side of the rectangle.

The height is

[tex]|7-1|=6 units[/tex]

To find the base, use the points (-2,7) and (-4,7) or (-2,1) and (-4,1).

The base is

[tex]|-2--4|=2 units[/tex]

Answer: The base is 2 units and the height is 6 units.

Step-by-step explanation:

You can plot the points  (-4, 7), (-2, 7), (-2, 1), and (-4, 1) and obtain the rectangle shown in the figure attached.

As you can see in the figure, the distance between the points of the base is:

[tex]d=\sqrt{(-2-(-4))^2+(1-1)^2}\\d=2[/tex]

Then the lenght of the base is 2 units

The distance between the points of the height is:

 [tex]d=\sqrt{(-2-(-2))^2+(1-7)^2}\\d=6[/tex]

Then the height is 6 units

3x + 6y = 36

+ 3x - 6y =0

------------------------

6x = 36

x = 36/6

x = 6

3(6) - 6y = 0

18 - 6y = 0

-6y = -18

y = 3

Answer:

Solution (6 ,3).

Step-by-step explanation:

Given : 3x + 6y = 36 and 3x - 6y = 0

To find : use the elimination method to solve the system of equations.

Solution : We have given

3x + 6y = 36 ------(1)

3x - 6y = 0------(2)

_______________       (On adding both equations)

6x + 0 = 36 .

On dividng both sides by 6

x = 6.

On plug x = 6 in equation 1

3 ( 6) + 6y  = 36.

18 + 6y = 36 .

On subtracting both sides by 18

6y = 36 -  18.

6y = 18

On dividing both sides by 6

y = 3

Solution (6 ,3)

Therefore, Solution (6 ,3).

Answer:  [tex]\bold{\dfrac{4\pm \sqrt{6}}{2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3}{y-2}-2=\dfrac{1}{y-1}\\\\\\\text{Multiply by the LCD (y-2)(y-1) to clear the denominator:}\\\\\dfrac{3}{y-2}(y-2)(y-1)-2(y-2)(y-1)=\dfrac{1}{y-1}(y-2)(y-1)\\\\\\3(y-1)-2(y-2)(y-1)=1(y-2)\\\\3y-3-2(y^2-3y+2)=y-2\\\\3y-3-2y^2+6y-4=y-2\\\\-2y^2+9y-7=y-2\\\\0=2y^2-8y+5\quad \rightarrow \quad a=2,\ b=-8,\ c=5\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-8)\pm \sqrt{(-8)^2-4(2)(5)}}{2(2)}\\\\\\.\ =\dfrac{8\pm \sqrt{64-40}}{2(2)}[/tex]

[tex].\ =\dfrac{8\pm \sqrt{24}}{2(2)}\\\\\\.\ =\dfrac{8\pm 2\sqrt{6}}{2(2)}\\\\\\.\ =\dfrac{4\pm \sqrt{6}}{2}[/tex]

8.25 rounded off to the nearest whole number is 8, because the digit after the decimal point (2) is less than 5, which implies that we do not increase the whole number part.

To round off 8.25 to the nearest whole number, we look at the digit to the right of the decimal point, which is 2. Since this digit is less than 5, we keep the digit before the decimal point as it is. Therefore, 8.25 rounded off to the nearest whole number is 8.

When rounding numbers, such as rounding off 0.028675 to 0.0287 or 92.85 to 92.8, a key rule to remember is that if the dropped digit is greater than or equal to 5, you round up; if less, you round down. Applying this principle, we see that because 2 is less than 5, 8.25 rounds down, leaving us with 8 as the rounded result.

Answer:

The correct answer option is 'then'.

Step-by-step explanation:

The "to prove" part of the information is the 'then' of the "if-then" statement.

For example, we have this problem:

[tex] y = 2 x - 1 [/tex]

If [tex] x = 3 [/tex], then find the value of y.

Here in this problem, we are asked that 'if' the value of x is true then prove it by substituting in the value.

Answer:

The answer is Then.

Step-by-step explanation:

The "to prove" part of the information is the THEN of the "if-then" statement.

If is the question like, it is not validated. You are asking something if it holds true.

For example: If it rains heavily, then water bodies fill up.

So, here you are proving that water bodies fill if rains are heavy.

Another example: If a = 3 and b = 6 then a+b = 9

We can see that 3+6=9

Then it is proved that a + b = 9

First we need to find 60% of 20,000 sq ft.

so 20,000 x .60 = 12,000 sq ft.

since the parking space needs to be 12,000 sq ft, you'd have 8,000 sq ft. of the 20,000 left to construct the building.

Answer:

[tex]8,000ft^2[/tex]

Step-by-step explanation:

If 60% of the land area is destined to be a parking area, the other 40% of the total 100% remains for the construction.

So what we need is to find how much 40% of the  [tex]20,000ft^2[/tex]  is:

[tex]\frac{20,000}{100}*40=200*40=8,000[/tex]

or what is the same

[tex]20,000*0.4=8,000[/tex]

The space left to construct the building is [tex]8,000ft^2[/tex]

Answer:

Factoring is written as the product of simpler expressions/factors.

Step-by-step explanation:

Factoring (called "Factorising" in the UK) is the process of finding the factors.

Factoring is the method of finding what to multiply together to get an expression.

It is like "splitting" an expression into a multiplication of simpler expressions.

Example: factor [tex]2y+6[/tex]

Both [tex]2y[/tex] and 6 have a common factor of 2:

[tex]2y[/tex]  is 2 × y

6 is 2 × 3

So we can factor the whole expression into:

[tex]2y+6 = 2(y+3)[/tex]

So [tex]2y+6[/tex]  has been "factored into" 2 and y+3.

The equation is [tex]\[ 130x + 150y = 1920 \end{cases} \][/tex]

Let's represent the number of months Lance lived in Portugal as x and the number of months he lived in Brazil as y.

Since Lance lived in Portugal for x months and learned 130 words per month, the total number of words he learned in Portugal is 130x.

Similarly, since Lance lived in Brazil for y months and learned 150 words per month, the total number of words he learned in Brazil is 150y.

We're given that the total number of words Lance learned is 1920. So, the system of equations representing this situation is:

[tex]\[ \begin{cases} 130x + 150y = 1920 \\x + y = 14 \end{cases} \][/tex]

The first equation represents the total number of words Lance learned, and the second equation represents the total number of months he spent in both countries combined.

Answer:

Distance - The number of units between two numbers or points, regardless of direction.

Inequality - Sentence showing a relationship between numbers that are not necessarily equal; uses the symbols >, <, ≥, ≤, or ≠

Opposite numbers - Two numbers that are the same distance from zero on the number line but in opposite directions.

Absolute Value - The distance from zero on the number line.

The question matches mathematics concepts like absolute value, inequality, opposite numbers, and distance.

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The old photocopier can make x manuals in an hour. The new photocopier can make 4x. Combined, they made 5x manuals in an hour.

In one hour they can make 1/28 of the manuals.

1/(28*5)=1/140 is the rate.

The new photocopier can make all the manuals in 4/140 or 35 hours.

The old one can make them in 140 hours.

The expression 7(3sqrt(2x)) - 3(3sqrt(16x)) - 3(3sqrt(8x)) simplifies to 3sqrt(2x) - 36sqrt(x) by first simplifying the square roots where possible, then distributing the coefficients, and finally combining like terms.

The expression given is 7(3sqrt(2x)) - 3(3sqrt(16x)) - 3(3sqrt(8x)). To simplify it, let's perform each operation step by step keeping in mind the properties of square roots and distributive property of multiplication.

Firstly, simplify inside the square roots where possible. sqrt(16x) = 4sqrt(x) and sqrt(8x) = 2sqrt(2)*sqrt(x) = 2*sqrt(2x). Now substitute these back into the equation:

7(3sqrt(2x)) - 3(3*4sqrt(x)) - 3(3*2sqrt(2x))

Now distribute the coefficients:

21sqrt(2x) - 36sqrt(x) - 18sqrt(2x)

Next, combine like terms.

21sqrt(2x) - 18sqrt(2x) - 36sqrt(x)

This results in:

3sqrt(2x) - 36sqrt(x)

Therefore, the simplified form of the expression is 3sqrt(2x) - 36sqrt(x).

The correct answer is (D).

Answer:   [tex]\bold{\dfrac{3\pm \sqrt{65}}{14}}[/tex]

Step-by-step explanation:

[tex]7x^2-3x=2\quad \rightarrow \quad 7x^2-3x-2=0\quad \rightarrow \quad a=7,\ b=-3,\ c=-2\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-3)\pm \sqrt{(-3)^2-4(7)(-2)}}{2(7)}\\\\\\.\ =\dfrac{3\pm \sqrt{9+56}}{14}\\\\\\.\ =\dfrac{3\pm \sqrt{65}}{14}[/tex]

Yeah, it seems the right answer!

well there’s 360 degrees in one circle so it’s just 270/360 which is 1/4 . you’re welcome and brainliest would be nice ty

Answer:

¾

Step-by-step explanation:

Your diagram shows that moving the hand 270° covered three of the divisions of the circle.

A circle consists of four equal parts, and you covered three of them.

Thus, 270° is ¾ of a complete turn.  

Semiannually means twice a year, so you multiple $67,000 by 2.

The annual salary is $134000

Semiannual is a term that describes something that is paid twice each year, typically once every six months.

Since semiannually salary is $67,000 so the annual salary will be

$67,000 x 2 = $134000

Answer:

Step-by-step explanation:

Is what you want equal to p/6? That's all that is written.

Answer:

[tex]\frac{p}{6}[/tex]

Step-by-step explanation:

An algebraic expression is any expression using variables, in this case, p.

40x-72 because 8×5x is 40x and 8×9 is 72

Answer:

0.35 cents

Step-by-step explanation:

8 pints in 1 gallon. 8 x .65/pint = 5.20.

5.20 (8-pints) - 4.85 (gallon jug) = .35

Answer:

Every day, Jason runs for 31 minutes and lifts weights for 43 minutes. How many minutes will Jason spend working out in 8 days?

A.  96

B.  592

C. 248

D.  82

Step-by-step explanation:

(31+43) x 8 =

74 x 8 = 592

Answer: The answer would be B!

Step-by-step explanation:

31 minutes for jogging + 43 minutes for weight lifting = 74 minutes in total !

73 minutes a day x 8 days = 592 minutes

Hope this helped ! :)

Answer:

1. b ,2.c ,3.b

Step-by-step explanation:

Answer:

51%

Step-by-step explanation:

Add up the tallies, as follows:  17+24+9+19.  Then divide the "cycling" tally (24) by this sum ( 69), obtaining the "observed probability that the customer will want to cycle"):  p = 24/69 = 34.7%.

The center of the circle that can be circumscribed about Triangle EFG with E(2,2), F(2,-2), and G(6,-2) is (2, -2).

To find the center of the circle circumscribed about triangle EFG, we can first find the midpoint of EF and the midpoint of FG.

These midpoints will lie on the perpendicular bisectors of EF and FG respectively.

The intersection of these bisectors will give us the center of the circle. Let's calculate it step-by-step:

Step 1: Find the midpoint of EF.

Midpoint of EF = ((2+2)/2, (2-2)/2) = (2, 0).

Step 2: Find the midpoint of FG.

Midpoint of FG = ((2+6)/2, (-2-2)/2) = (4, -2).

Step 3: Find the equation of the perpendicular bisector of EF.

The slope of EF = (0 - 2)/(2 - 2) = undefined. The midpoint of EF is (2, 0).

Hence, the equation of the perpendicular bisector of EF is x = 2.

Step 4: Find the equation of the perpendicular bisector of FG.

The slope of FG = (-2 - (-2))/(6 - 2) = 0. The midpoint of FG is (4, -2).

Hence, the equation of the perpendicular bisector of FG is y = -2.

Step 5: Solve the equations of the perpendicular bisectors to find the center of the circle. Since x = 2 and y = -2, the center of the circle is (2, -2).

Final answer:

To find the center of the circle that can be circumscribed about Triangle EFG, use the midpoint formula and equations of the perpendicular bisectors.

Explanation:

To find the center of the circle that can be circumscribed about Triangle EFG with coordinates E(2, 2), F(2, -2), and G(6,-2), we can use the following steps:

Find the midpoint of each side of the triangle, which will be the center of the circle.

Use the midpoint formula to find the coordinates of the midpoints of EF and FG.

The center of the circle will be the point where the perpendicular bisectors of each side intersect.

Find the equation of the perpendicular bisectors of EF and FG.

Solve the system of equations formed by the equations of the perpendicular bisectors to find the coordinates of the center of the circle.

The center of the circle that can be circumscribed about Triangle EFG is (-2/3, -4/3).

Concept is trigonometry. The tangent of 30° is √3.

To find the tangent of 30°, we can use a special right triangle. One type of special right triangle is a 30-60-90 triangle. In this triangle, the ratio of the lengths of the sides opposite the angles are 1:√3:2.

Since we want to find the tangent of 30°, which is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle, we can set up the equation:

tan 30° = opposite/adjacent = (√3)/1 = √3

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Answer:

1) [tex]b=12[/tex]

2) [tex]tan(22.6\°)=\frac{a}{12}[/tex] (Third option)

Step-by-step explanation:

Remember that:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]

1) Given that:

[tex]cos(22.6\°)=\frac{b}{13}[/tex]

You know that b is the adjacent side of the right triangle.

To solve for b you must multiply both sides of the expression by 13. Then, the value of b is:

[tex]13*cos(22.6\°)=\frac{b}{13}*13\\13*cos(22.6\°)=b\\b=12[/tex]

2) Then, you have that the equation correctly uses the value of b  ( adjacent side) to solve for a (opposite side) is:

[tex]tan(22.6\°)=\frac{a}{12}[/tex]

The value for b is 12 and  [tex]tan(22.6 ^{\circ \:} )=\frac{a}{12}\\[/tex].

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  

For solving this question, you need to apply trigonometric ratios for the right triangle.

This question informs [tex]cos (22.6)=\frac{b}{13}[/tex]. Here, you should remember that cos of an angle is calculated by the ratio between the adjacent side from the angle and the hypotenuse of the right triangle. Therefore, [tex]cos=\frac{adj}{hyp}[/tex].

From a calculator, you find cos(22.6°)=0.92321. Thus,

                                       [tex]cos (22.6)=\frac{b}{13}\\ \\ 0.92321=\frac{b}{13}\\ \\ b= 0.92321*13\\ \\ b=12.002\\ \\ b=12[/tex]

The second part of question asks how to find the tangent value. The tangent can be calculated by formula presented below:

                               [tex]tan(\alpha )=\frac{opposite \;side\;angle}{adjacent\;side\;angle}[/tex]

For the angle 22.6°, you have:

Therefore,  [tex]tan(22.6 ^{\circ \:} )=\frac{a}{12}\\[/tex]

Learn more about the trigonometric ratios here:

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Answer:

lay the net out with numbers then add all of them

Step-by-step explanation:

Answer:

Lay the net out with the dimensions then multiply for each shape and add all of the areas to get the total surface area of your prism.

Step-by-step explanation:

I just got it correct on my online class.

Answer:

B

Step-by-step explanation:

When x=0,

Y=1/2(0)+1

Y=1

Look for the line with the point (0,1)

Answer:

4/5

Step-by-step explanation:

Answer: [tex]m= \frac{4}{5}[/tex] or [tex]m= 0.8[/tex]

(0,0) = (x1,y1)

(5,4) = (x2,y2)

Slope= [tex]\frac{y2-y1}{x2-x1}[/tex]

         = [tex]\frac{4-0}{5-0}[/tex]

         = [tex]\frac{4}{5}[/tex]

As decimal

         = [tex]0.8[/tex]

Answer:

A

Step-by-step explanation:

A is correct. Subtract 8 from both sides and then divide both sides by 3.

The inequality 3x + 8 ≥ 11 is represented by a line having a close circle at

x = 1 and going towards infinity.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, an inequality of line which is 3x + 8 ≥ 11.

3x ≥ 11 - 8.

3x ≥ 3.

x ≥ 3/3.

x ≥ 1.

This will be represented on a line with a close circle at x = 1 and the line will go towards infinity.

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Answer:   32

Step-by-step explanation:

[tex]F(C)=\dfrac{9}{5}C+k\\\\-40=\dfrac{9}{5}(-40)+k\\\\-40=9(-8)+k\\\\-40=-72+k\\\\.\quad32=k[/tex]

Answer:

k = 32

Step-by-step explanation:

To get the value of k from expression:

[tex]F(C) = \frac{9}{5}C +k[/tex]

for F = -40 and C = -40, then:

[tex]-40 = \frac{9}{5}(-40)+k[/tex]

[tex]k =-40+\frac{9}{5}.40[/tex]

[tex]k = 72 - 40[/tex]

[tex]k = 32[/tex]

therefore, k should be 32 to get these answers.